Dry, itchy eyes for that long certainly sounds like allergies to me. Know that allergies can "come and go". And you can develop allergies to certain things out of the blue, where before you have tolerated it. I'm not aware of allergies being heriditary. Allergies are unpredictable! I have season allergies (mostly in the fall) and some years I am in agony, and other years it's barely noticeable.
I would try just eye drops before I started giving him oral medicaiton. If it's just his eyes that are bothering him at this point, eye drops should do the trick.
If he develops nasal/sinus irritation, consider a neti pot. They are amazing! It might be too difficult to get a 2 yo told use one, but keep them in mind for when he gets older. Good luck!